arXiv subjects

Ian Kash

Publications and source records attributed to Ian Kash.

8 recordsLinked to original sources

arXiv2025

Online Job Assignment

Motivated primarily by applications in cloud computing, we study a simple, yet powerful, online allocation problem in which jobs of varying durations arrive over continuous time and must be assigned immediately and irrevocably to one of the available offline servers. Each server has a fixed initial capacity, with assigned jobs occupying one unit for their duration and releasing it upon completion. The algorithm earns a reward for each assignment upon completion. We consider a general heterogeneous setting where both the reward and duration of a job depend on the job-server pair. The objective of the online algorithm is to maximize the total collected reward, and remain competitive against an omniscient benchmark that knows all job arrivals in advance. Our main contribution is the design of a new online algorithm, termed Forward-Looking BALANCE (FLB), and using primal-dual framework to establish that it is (asymptotically) optimal-competitive. This meta-algorithm has two main primitives: (i) keeping track of the capacity used for each server at each time and applying a penalty function to this quantity, and (ii) adjusting the reward of assigning a job to a server by subtracting the total penalty of a particularly chosen subset of future times, in contrast to just looking at the current time. The FLB algorithm then assigns the arriving job to the server with the maximum adjusted reward. If R and D are the ratios of maximum over minimum rewards and durations, we show that the FLB algorithm obtains an asymptotic competitive ratio of ln(RD)+3lnln(max(R,D))+O(1). We further show this bound has optimal dependencies on all the parameters. Our main analysis combines a novel dual-fitting technique, which leverages the configuration LP benchmark for this problem, and a novel inductive argument to establish the capacity feasibility of the algorithm, which might be of independent interest.

cs.DS↗

arXiv2025

Peer Prediction with More Signals than Reports

Peer prediction mechanisms are typically proposed and analyzed under the assumption that the report and signal spaces are identical. In practice, however, agents often observe richer information which they then map to a coarser report space. Motivated by this discrepancy between theory and practice, we initiate the study of peer prediction mechanisms with signal spaces that are richer than the report space. We begin by formalizing a model with real-valued signals and binary reports. In this setting, it is natural to study symmetric threshold strategies, where agents map their signals to binary reports according to a single real-valued threshold. For several well-known binary-report peer prediction mechanisms, we show that most equilibria under the original assumption of binary signals are no longer equilibria in our model. Furthermore, dynamic analysis proves that some of the remaining thresholds are unstable. These results extend beyond real-valued signals and binary reports to settings where the signal space is finer-grained than the report space. While the results above suggest important limitations for the deployment of existing peer prediction mechanisms in practice, we also use them to develop a new, more robust mechanism. This mechanism generates a larger number of stable threshold equilibria under our model, thus allowing the designer more flexibility in choosing how agents map their signals to reports.

cs.GT↗

arXiv2024

Decentralized Fair Division

Fair division is typically framed from a centralized perspective. However, in practice resource allocation often occurs via decentralized networks. We study a decentralized variant of fair division inspired by altruistic dynamics observed in behavioral economics and other practical settings. We develop an approach for decentralized fair division and compare it with a centralized approach with respect to fairness and social welfare guarantees. Our decentralized model can be seen as a relaxation of previous models of sequential exchange, in light of impossibility results concerning the inability of those models to achieve desirable outcomes. We find that the two models of resource allocation offer contrasting fairness and social welfare guarantees, and map out how these guarantees depend on valuations and other model parameters. We further show conditions under which a mix of the two approaches outperforms either approach in isolation. Despite the simplicity of our decentralized model, we show that under appropriate conditions it can ensure high-quality allocative decisions in an efficient fashion.

cs.GT↗

arXiv2021

Fairness Through Counterfactual Utilities

Group fairness definitions such as Demographic Parity and Equal Opportunity make assumptions about the underlying decision-problem that restrict them to classification problems. Prior work has translated these definitions to other machine learning environments, such as unsupervised learning and reinforcement learning, by implementing their closest mathematical equivalent. As a result, there are numerous bespoke interpretations of these definitions. Instead, we provide a generalized set of group fairness definitions that unambiguously extend to all machine learning environments while still retaining their original fairness notions. We derive two fairness principles that enable such a generalized framework. First, our framework measures outcomes in terms of utilities, rather than predictions, and does so for both the decision-algorithm and the individual. Second, our framework considers counterfactual outcomes, rather than just observed outcomes, thus preventing loopholes where fairness criteria are satisfied through self-fulfilling prophecies. We provide concrete examples of how our counterfactual utility fairness framework resolves known fairness issues in classification, clustering, and reinforcement learning problems. We also show that many of the bespoke interpretations of Demographic Parity and Equal Opportunity fit nicely as special cases of our framework.

cs.LG↗

arXiv2021

Buying Data Over Time: Approximately Optimal Strategies for Dynamic Data-Driven Decisions

We consider a model where an agent has a repeated decision to make and wishes to maximize their total payoff. Payoffs are influenced by an action taken by the agent, but also an unknown state of the world that evolves over time. Before choosing an action each round, the agent can purchase noisy samples about the state of the world. The agent has a budget to spend on these samples, and has flexibility in deciding how to spread that budget across rounds. We investigate the problem of choosing a sampling algorithm that optimizes total expected payoff. For example: is it better to buy samples steadily over time, or to buy samples in batches? We solve for the optimal policy, and show that it is a natural instantiation of the latter. Under a more general model that includes per-round fixed costs, we prove that a variation on this batching policy is a 2-approximation.

cs.GT↗

arXiv2019

Partial Verification as a Substitute for Money

Recent work shows that we can use partial verification instead of money to implement truthful mechanisms. In this paper we develop tools to answer the following question. Given an allocation rule that can be made truthful with payments, what is the minimal verification needed to make it truthful without them? Our techniques leverage the geometric relationship between the type space and the set of possible allocations.

cs.GT↗

arXiv2016

Optimal Auctions with Restricted Allocations

We study the problem of designing optimal auctions under restrictions on the set of permissible allocations. In addition to allowing us to restrict to deterministic mechanisms, we can also indirectly model non-additive valuations. We prove a strong duality result, extending a result due to Daskalakis et al. [2015], that guarantees the existence of a certificate of optimality for optimal restricted mechanisms. As a corollary of our result, we provide a new characterization of the set of allocations that the optimal mechanism may actually use. To illustrate our result we find and certify optimal mechanisms for four settings where previous frameworks do not apply, and provide new economic intuition about some of the tools that have previously been used to find optimal mechanisms.

cs.GT↗

arXiv2007

Efficiency and Nash Equilibria in a Scrip System for P2P Networks

A model of providing service in a P2P network is analyzed. It is shown that by adding a scrip system, a mechanism that admits a reasonable Nash equilibrium that reduces free riding can be obtained. The effect of varying the total amount of money (scrip) in the system on efficiency (i.e., social welfare) is analyzed, and it is shown that by maintaining the appropriate ratio between the total amount of money and the number of agents, efficiency is maximized. The work has implications for many online systems, not only P2P networks but also a wide variety of online forums for which scrip systems are popular, but formal analyses have been lacking.

cs.GT↗